{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 第九周作业--极线几何与立体视觉"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "问题描述\n",
    "一、 问题描述：\n",
    "（本周共计5个必做作业）\n",
    "1. 试画图说明极线几何关系，并指出极点、极线所在，解释极线约束。\n",
    "2. 结合本质矩阵的定义，说明本质矩阵的意义，同时思考与上一周中平面点对应透视矩阵的区别。\n",
    "3. 说明三维重构的步骤，并指出输入及输出要求。\n",
    "4. 说明特征匹配的步骤，进一步说明基于k-d树的特征匹配方法的思路。\n",
    "5. 说明RANSAC方法的基本思想及实施步骤。 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.试画图说明极线几何关系，并指出极点、极线所在，解释极线约束。"
   ]
  },
  {
   "attachments": {
    "%E9%80%89%E5%8C%BA_020.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "答：![%E9%80%89%E5%8C%BA_020.png](attachment:%E9%80%89%E5%8C%BA_020.png)\n",
    "如图，M为三维空间中的点，C1和C2为空间中两台摄像机所在位置，MC1与成像平面交于m1，MC2与成像平面交于m2，C1C2连线与两成像平面分别交于e1和e2。\n",
    "\n",
    "基线：左右像机光心连线，即C1C2连线；\n",
    "\n",
    "极平面：空间点，两像机光心决定的平面，即平面MC1C2；\n",
    "\n",
    "极点：基线与两摄像机图像平面的交点,即点e1，e2；\n",
    "\n",
    "极线：极平面与图像平面交线，即m1e1 和 m2e2;\n",
    "\n",
    "极线约束：匹配点必须在极线上。由匹配点既属于极平面,又属于图像平面，因此属于它们的交线上，即极线上。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.结合本质矩阵的定义，说明本质矩阵的意义，同时思考与上一周中平面点对应透视矩阵的区别。"
   ]
  },
  {
   "attachments": {
    "%E9%80%89%E5%8C%BA_021.png": {
     "image/png": "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"
    },
    "%E9%80%89%E5%8C%BA_022.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "答：本质矩阵 E 可以将空间中的一点在左相机和右相机中的成像关联起来，由极线几何可以推导得到如下公式：![%E9%80%89%E5%8C%BA_021.png](attachment:%E9%80%89%E5%8C%BA_021.png)\n",
    "将中间部分用记为E，如图：![%E9%80%89%E5%8C%BA_022.png](attachment:%E9%80%89%E5%8C%BA_022.png)\n",
    "即E = [t]<sub>x</sub>R，E就是本质矩阵。在此基础上求出 R 和 t，得到两个相机之间的姿态和位置关系。\n",
    "\n",
    "透视变换是从某个投射中心将源图像平面上的信息投射到另一图像平面上，透视矩阵的作用是实现从源平面到新图像平面的转换。而本质矩阵的作用是将空间点在两个像平面上的投影点对应起来。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.说明三维重构的步骤，并指出输入及输出要求。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 答：\n",
    "1）提取特征点，建立特征匹配，可以通过sift或者Harris进行特征点提取和匹配，输入：2张图片；输出：两张图片匹配的特征点；\n",
    "2）计算视差，输入2张图片几匹配额特征点；输出：每个像素点的视差；\n",
    "3）计算世界坐标，由上一步的视差，可以进一步计算每个点的世界坐标，输入：图片以及每个像素点的视差，视差：每个像素点的世界坐标；\n",
    "4）三角剖分，采用经典的Delauney算法。\n",
    "5）三维重构，基于计算坐标，采用OpenGL绘制三角片，完成三维重构。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.说明特征匹配的步骤，进一步说明基于k-d树的特征匹配方法的思路。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 答：在特征匹配前，先用sift\\harris等方法进行特征点提取，得到特征点的描述向量，根据特征点的描述子对两张图片上的特征点进行匹配，得到匹配结果。采用k-d树进行特征匹配的方法如下：\n",
    "- k-d树建立：选择合适的分割维度，选择中值节点作为分割节点。分割维度的选择遵循的原则是，选择范围最大的维度，也即是方差最大的纬度作为分割维度；分割节点的选择原则是，将这一维度的数据进行排序，选择正中间的节点作为分割节点，确保节点左边的点的维度值小于节点的维度值，节点右边的点的维度值大于节点的维度值。重复上述步骤，直至左右分支都到达叶子结点。\n",
    "- k-d树最近领查询算法：\n",
    "1)首先按照二叉检索的方式，检索到在同一子空间的叶子结点，作为最近邻的近似点；\n",
    "2)设该叶子节点为最近邻节点，并计算与目标点之间的距离d1。\n",
    "3)根据检索路径进行回溯，以目标点为圆心，以上一步骤获得的距离d1为半径，画圆，判断回溯点所在的超平面是否与该圆相交，若没有则该回溯点的另外一侧比不存在最近邻点，无需检索，否则需要调到另外一侧节点空间进行检索，并将相关点加入回溯路径。\n",
    "4)重复2与3步骤，直至回溯完所有节点，得到最终的结果。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 5. 说明RANSAC方法的基本思想及实施步骤。 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "答： RANSAC方法的基本思想：\n",
    "RANSAC通过反复选择数据中的一组随机子集来达成目标。被选取的子集被假设为局内点，并用下述方法进行验证：\n",
    "1)有一个模型适应于假设的局内点，即所有的未知参数都能从假设的局内点计算得出；\n",
    "2)用1中得到的模型去测试所有其他的数据，如果某个点适用于估计的模型，认为它也是局内点；\n",
    "3)如果足够多的点被归类为假设的局内点，那么估计的模型足够合理；\n",
    "4)然后，用所有的假设的局内点重新估计模型，因为它只是被初始化的假设局内点估计过；\n",
    "5)最后，通过估计局内点与模型的错误率来评估模型。\n",
    "这个过程被重复执行固定的次数，每次产生的模型要么因为局内点太少二被舍弃，要么因为比现有的模型更好而被选用。\n",
    "与最小二乘法相比，RANSAC在数据噪声较大的情况下，会取得更好的结果。"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python tf1.14",
   "language": "python",
   "name": "tf1.14"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
